This competing continuation proposal is concerned with the analysis of epidemiologic studies of cancer in which various temporal variables play an important role. Time-related factors include attained age, age at exposure, duration of exposure, latency, time since start of observation, birth cohort, and calendar year. Particular emphasis is on the analysis of studies involving extended exposure histories with intensities that vary over time and between individuals. The resulting cancer risk is not easily summarized by a single exposure index, and attempts to look at the modifying effect of temporal variables are complicated by the problem of deciding whether "age at exposure" now means age at first exposure, last exposure, or some weighted average of all exposures. We plan to pursue these problems with a combination of methodological developments and applications. The methodologic research includes A. Methods for fitting various models of carcinogenesis and comparison of their performance using computer simulation; particular attention will be paid to the multistage and Moolgavkar-Knudson two-stage model, a new model we propose for radiation carcinogenesis, and the incorporation of simple compartment models for toxicokinetics. B . Methods for fitting nonproportional hazards models, based on nonparametric estimation of baseline hazard functions and use of external rates; C. Descriptive methods for visualizing the evolution of risk over time and for testing the fit of parametric models; and D. Exploration of alternative designs for nested case-control studies. The methods will be illustrated by applications to various data sets, with particular emphasis on a number of epidemiologic and experimental studies relating to radiation and cancer.